Question

Mrs Grey is buying decorative ribbon of three different colors: blue, silver, and yellow. Blue ribbon is sold in rolls of 15 meters, silver is sold in rolls of 12 meters, and yellow comes in rolls of 20 meters. She needs to have the same length of each ribbon. What is the smallest number of rolls of each type that she should buy?

Answer 1

Answer:

4 rolls of blue ribbon,

5 rolls of silver ribbon,

3 rolls of yellow ribbon.

Step-by-step explanation:

We have been given that Mrs Grey is buying decorative ribbon of three different colors: blue, silver, and yellow. Blue ribbon is sold in rolls of 15 meters, silver is sold in rolls of 12 meters, and yellow comes in rolls of 20 meters.

As Mrs. Grey needs to have same length of each ribbon, so we will find the least common multiple of 15, 12 and 20.

Multiples of 15 are: 15, 30, 45, 60, 75, 90,...

Multiples of 12 are: 12, 24, 36, 48, 60, 72, 84,...

Multiples of 20 are: 20, 40, 60, 80,100,...

We can see that 60 is the least common multiple of 15, 12 and 20.

$\text{The smallest number of rolls of blue ribbon}=\frac{60}{15}=4$

Therefore, Mrs. Grey should buy 4 rolls of blue ribbon.

$\text{The smallest number of rolls of silver ribbon}=\frac{60}{12}=5$

Therefore, Mrs. Grey should buy 5 rolls of silver ribbon.

$\text{The smallest number of rolls of yellow ribbon}=\frac{60}{20}=3$

Therefore, Mrs. Grey should buy 3 rolls of yellow ribbon.